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No.2202 贅沢てりたまチキン

レベル : / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 150
作問者 : H20 / テスター : 👑 p-adic
お気に入りにしたユーザー ProblemId : 9114 / 自分の提出
問題文最終更新日: 2026-10-16 02:40:21
Luxury Teritama Chicken
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yukicoder contest 375 (順位表) の他の問題:

Problem Statement

Yukiko Railway has $N$ stations $($ station $1,$ station $2, \ldots,$ station $N )$ and $M$ pairs of $2$ tracks.

The $i$-th pair consists of 2 tracks laid so as to bidirectionally connect the surface level of station $A_i$ with the underground level of station $B_i$, and the underground level of station $A_i$ with the surface level of station $B_i$, where these are $2$ different stations.

Determine whether it is possible to travel back and forth between the surface level and the underground level of each station using only the tracks of the railway.

Input

$N\ M$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_M$ $B_M$

Constraints

  • $ 1 \le N \le 2\times10^{5}$
  • $ 0 \le M \le \min(2\times10^{5},\frac{N(N-1)}{2})$
  • $ 1 \le A_i, B_i \le N$
  • $ A_i \neq B_i$
  • $\{A_i,B_i\} \neq \{A_j,B_j\}$ ($1 \leq i \neq j \leq M$)
  • All inputs are integers.

Output

If it is possible to travel back and forth between the surface level and the underground level of each station using only the tracks of the railway, print Yes; otherwise, print No.

Print a newline at the end.

Sample

Sample 1
Input
4 4
1 2
2 3
3 4
4 2
Output
Yes

You can move from the surface to the underground of each station as follows. Considering the reverse direction, you can also move from the underground to the surface, so travel back and forth is possible.

Station $1$ surface → Station $2$ underground → Station $3$ surface → Station $4$ underground → Station $2$ surface → Station $1$ underground

Station $2$ surface → Station $3$ underground → Station $4$ surface → Station $2$ underground

Station $3$ surface → Station $4$ underground → Station $2$ surface → Station $3$ underground

Station $4$ surface → Station $2$ underground → Station $3$ surface → Station $4$ underground

Sample 2
Input
5 4
1 2
2 3
3 4
5 3
Output
No

For every station, it is impossible to travel back and forth between its surface level and its underground level.

Sample 3
Input
6 5
1 2
2 3
3 4
4 5
5 1
Output
No

At station $6$, it is impossible to travel back and forth between the surface level and the underground level.

As in this case, if there is even $1$ station where travel back and forth is impossible, print No.

Sample 4
Input
9 10
1 3
9 4
3 6
2 6
6 8
3 8
5 4
7 4
5 9
2 8
Output
Yes

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